You have a scale. On one side of the scale is a brick. On the other side of the scale is half of a brick and a ¾ lb weight. If the scale is balanced what is the weight of the brick in pounds.
let the weight of the brick be x lbs
x = (1/2)x + 3/4
times 4
4x = 2x + 3
carry on
To solve this problem, we need to use the concept of balancing weights on a scale. Let's break down the given information:
- On one side of the scale, we have a whole brick.
- On the other side of the scale, we have half of a brick and a ¾ lb weight.
Since the scale is balanced, we can deduce that the weight on both sides must be equal.
Let's assign variables to the unknown quantities:
- Let's call the weight of the brick "x" (in pounds).
With this information, we can set up an equation representing the balance of weights on the scale:
1 brick = ½ brick + ¾ lb
To solve this equation, we need to isolate the variable "x" (the weight of the brick). Here's how we can proceed:
1. Subtract ½ brick from both sides of the equation:
1 brick - ½ brick = ¾ lb
We can simplify this equation by calculating the weight of half a brick:
½ brick = ½ x = x/2
Substituting this into our equation:
1 brick - x/2 = ¾ lb
2. To get rid of the fraction, we can multiply every term in the equation by 2:
2(1 brick) - 2(x/2) = 2(¾ lb)
Simplifying further:
2 bricks - x = 1.5 lb
3. Move the x term to one side of the equation by subtracting it from both sides:
2 bricks - x - 2 bricks = 1.5 lb - 2 bricks
This simplifies to:
- x = 1.5 lb - 2 bricks
4. Now, we need to calculate the weight of two bricks. Let's assume the weight of one brick is "w" pounds. Therefore, the weight of two bricks is 2w pounds.
Since we don't know the weight of one brick, let's represent it with "w" in our equation:
- x = 1.5 lb - 2w
5. At this point, we have an equation in terms of the weight of the brick, "x," and the weight of two bricks, "2w."
However, to find the weight of the brick, we need to know the weight of two bricks. Unfortunately, the problem doesn't provide us with that information.
Therefore, with the given information, we cannot determine the weight of the brick.